Acceleration

The quantity that describes the rate of change of velocity in a given time interval is called acceleration.

The magnitude of the average acceleration is calculated by dividing the total change in an object’s velocity by the time interval in which the change occurs.

Acceleration

A shuttle bus slows down with an average acceleration of -1.8 m/s2. How long does it take the bus to slow from 9.0 m/s to a complete stop?

As the shuttle bus comes to a sudden stop to avoid hitting a dog, it accelerates uniformly at −4.1 m/s2 as it slows from 9.0 m/s to 0.0 m/s. Find the time interval of acceleration for the bus.

A car traveling at 7.0 m/s accelerates uniformly at 2.5 m/s2 to reach a speed of 12.0 m/s. How long does it take for this acceleration to occur?

With an average acceleration of −1.2 m/s2, how long will it take a cyclist to bring a bicycle with an initial speed of 6.5 m/s to a complete stop?

Turner’s treadmill runs with a velocity of −1.2 m/s and speeds up at regular intervals during a half-hour workout. After 25 min, the treadmill has a velocity of −6.5 m/s. What is the average acceleration of the treadmill during this period?

Suppose a treadmill has an average acceleration of 4.7x10−3 m/s2.

a) How much does its speed change after 5.0 min?

b) If the treadmill’s initial speed is 1.7 m/s, what will its final speed be?

Acceleration has direction and magnitude

When the velocity in the positive direction is increasing, the acceleration is positive, as at point A. When the velocity is constant, there is no acceleration, as at point B. When the velocity in the positive direction is decreasing, the acceleration is negative, as at point C.

MOTION WITH CONSTANT ACCELERATION

The velocity increases by exactly the same amount during each time interval. Thus, the acceleration is constant. Because the velocity increases for each time interval, the successive change in displacement for each time interval increases.

How far can an object travel with constant acceleration?

*We know that the average velocity is equal to displacement divided by the time interval.

*For an object moving with constant acceleration, the average velocity is equal to the average of the initial velocity and the final velocity.

We can set the expressions for average velocity equal to each other.

Therefore;

This is formula of displacement with constant acceleration.

A racing car reaches a speed of 42 m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5 s later. Find the distance that the car travels during braking.

A car accelerates uniformly from rest to a speed of 6.6 m/s in 6.5 s. Find the distance the car travels during this time.

When Maggie applies the brakes of her car, the car slows uniformly from 15.0 m/s to 0.0 m/s in 2.50 s. How many meters before a stop sign must she apply her brakes in order to stop at the sign?

A driver in a car traveling at a speed of 21.8 m/s sees a cat 101 m away on the road. How long will it take for the car to accelerate uniformly to a stop in exactly 99 m?

A car enters the freeway with a speed of 6.4 m/s and accelerates uniformly for 3.2 km in 3.5 min. How fast (in m/s) is the car moving after this time?

What will the final velocity be with constant acceleration after t time?

By rearranging the equation for acceleration, we can find a value for the final velocity.

Cross multiply change in t;

Transpose initial velocity;

This is formula of final velocity with constant acceleration after t time.

If you want to know the displacement of an object moving with constant acceleration over some certain time interval, you can obtain another useful expression for displacement by substituting the expression for vf into the expression for Δx.

This is formula of displacement without vf.

A plane starting at rest at one end of a runway undergoes a uniform acceleration of 4.8 m/s2 for 15 s before takeoff. What is its speed at takeoff? How long must the runway be for the plane to be able to take off?

A car with an initial speed of 6.5 m/s accelerates at a uniform rate of 0.92 m/s2 for 3.6 s. Find the final speed and the displacement of the car during this time.

An automobile with an initial speed of 4.30 m/s accelerates uniformly at the rate of 3.00 m/s2. Find the final speed and the displacement after 5.00 s.

A car starts from rest and travels for 5.0 s with a constant acceleration of −1.5 m/s2. What is the final velocity of the car? How far does the car travel in this time interval?

A driver of a car traveling at 15.0 m/s applies the brakes, causing a uniform acceleration of −2.0 m/s2. How long does it take the car to accelerate to a final speed of 10.0 m/s? How far has the car moved during the braking period?

What will the final velocity be with constant acceleration after x displacement?

This is formula of vf after displacement of x with constant velocity.

A person pushing a stroller starts from rest, uniformly accelerating at a rate of 0.5 m/s2. What is the velocity of the stroller after it has traveled 4.75 m?

A car traveling initially at +7.0 m/s accelerates uniformly at the rate of +0.80 m/s2 for a distance of 245 m.a) What is its velocity at the end of the acceleration?b) What is its velocity after it accelerates for 125 m?c) What is its velocity after it accelerates for 67 m?

A car accelerates uniformly in a straight line from rest at the rate of 2.3 m/s2.a) What is the speed of the car after it has traveled 55 m?b) How long does it take the car to travel 55 m?

A motorboat accelerates uniformly from a velocity of 6.5 m/s to the west to a velocity of 1.5 m/s to the west. If its acceleration was 2.7 m/s2 to the east, how far did it travel during the acceleration?

An aircraft has a liftoff speed of 33 m/s. What minimum constant acceleration does this require if the aircraft is to be airborne after a take-off run of 240 m?

A certain car is capable of accelerating at a uniform rate of 0.85 m/s2. What is the magnitude of the car’s displacement as it accelerates uniformly from a speed of 83 km/h to one of 94 km/h?