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Honors Physics Glencoe Science, 2005 Slide 2 Change in time- ending time minus initial time t = t f - t i Change in velocity- final velocity minus initial velocity v = v f - v i Average acceleration- change in velocity between two distinct time intervals = v/ t = (v f - v i )/(t f - t i )(m/s 2 ) Instantaneous acceleration- change in velocity at an instant in time Only found by determining the tangent of a curve on a velocity-time graph Slide 3 Shows an object slowing down, speeding up, without motion, or at constant motion Slide 4 Represents motion graphically Plots the velocity versus the time of the object Slide 5 Sometimes we have an initial velocity Like when we pull through a stop light as it turns green Our acceleration formula can be rearranged v= t v f - v i = t If we are looking for the final velocity, then we multiply the acceleration by the time and add the initial velocity v f = t + v i Slide 6 A bus that is traveling at 30.0km/h speeds up at a constant rate of 3.5m/s 2. What velocity does it reach 6.8s later? Convert all to terms of m and s: (30.0km/h)(1000m/km)(1h/3600s)=v i Define known & unknown: a=3.5m/s 2 v i =8.33m/s t=6.8sv f =? Choose the appropriate equation v f = t + v i Rearrange if necessary (it is not in this case) Plug & Chug v f =(3.5m/s 2 )(6.8s)+(8.33m/s) v f =32.13m/s Slide 7 Looking at a position-time graph, we can find: Figure 3-9 Velocity (slope) Specific positions at specific times From our original velocity equation, v= d/ t, we can find that d=v t The area under the line in a velocity-time graph is v t, which is the displacement! Figure 3-10 Slope is v/ t, which is acceleration! Slide 8 Position (d f ) of an object under acceleration can be found with: d f =at 2 (m/s 2 )(s 2 )=m If there is an initial distance that we need to add, then: d f =d i +at 2 (m)+(m/s 2 )(s 2 )=m If there is an initial velocity, then we can also include that term! d f =d i +v i t+at 2 (m)+(m/s)(s)+(m/s 2 )(s 2 )=m This equation is only useful if time of travel is known Slide 9 Unlike the prior equation, sometimes time is not known, so we need to relate velocity to distance traveled v f 2 =v i 2 +2a(d f -d i )(m/s) 2 =(m/s) 2 +(m/s 2 ) (m-m) Slide 10 EquationVariablesInitial Conditions v f = t + v i v f, , t vivi d f =d i +v i t+at 2 d f, t, ad i, v i v f 2 =v i 2 +2a(d f -d i )v f, a, d f v i, d i Slide 11 A race car travels on a racetrack at 44m/s and slows at a constant rate to a velocity of 22m/s over 11s. How far does it move during this time? Define known & unknown: v i =44m/sv f =22m/s t=11s d=? a=? Choose the appropriate equation We need to find first v f = t + v i Rearrange if necessary =(-v i +v f )/ t Plug & Chug =(-44m/s+22m/s)/(11s) =-2m/s 2 Slide 12 Now that we have , we can solve for d f Define known & unknown: v i =44m/sv f =22m/s t=11sa=-2m/s 2 d=? Choose the appropriate equation d f =d i +v i t+at 2 Rearrange if necessary Plug & Chug d f =(0m)+(44m/s)(11s)+(-2m/s 2 )(11s) 2 d f =363m Slide 13 A car accelerates at a constant rate from 15m/s to 25m/s while it travels a distance of 125m. How long does it take to achieve this speed? Define known & unknown: v i =15m/sv f =25m/s t=?a=? d=125m Choose the appropriate equation We need to find first, but dont know time v f 2 =v i 2 +2a(d f -d i ) Rearrange if necessary a=(v f 2 -v i 2 )/(2 d) Plug & Chug a=((25m/s) 2 -(15m/s) 2 )/((2)(125m)) a=1.6m/s 2 Slide 14 Now that we have , we can solve for t Define known & unknown: v i =15m/sv f =25m/s t=?a=1.6m/s 2 d=125m Choose the appropriate equation v f = t + v i Rearrange if necessary (v f -v i )/ = t Plug & Chug (25m/s-15m/s)/(1.6m/s 2 )= t t=6.3s Slide 15 Free Fall- an object falling only under the influence of gravity Acceleration due to gravity- an object speeds up due to the Earths gravitational pull g=9.8m/s 2 Gravity is a specific kind of acceleration: like a quarter is a specific kind of money Gravity always points toward the center of the Earth Slide 16 As gravity (g) is a kind of acceleration (a), we can replace all of the as with g This can only be done if the object is in free fall EquationVariablesInitial Conditions v f =g t + v i v f, t vivi d f =d i +v i t+gt 2 d f, td i, v i v f 2 =v i 2 +2g(d f -d i )v f, d f v i, d i Slide 17 A construction worker accidentally drops a brick from a high scaffold. What is the velocity of the brick after 4.0s? Define known & unknown: v i =0m/sv f =? t=4.0sg=9.8m/s 2 d=? Choose the appropriate equation v f =g t + v i Rearrange if necessary (not necessary) Plug & Chug v f =(9.8m/s 2 )(4.0s)+(0m/s) v f =39.2m/s Slide 18 A construction worker accidentally drops a brick from a high scaffold. How far does the brick fall during this time? Define known & unknown: v i =0m/sv f =39.2m/s t=4.0sg=9.8m/s 2 d=? Choose the appropriate equation d f =d i +v i t+gt 2 Rearrange if necessary (not necessary) Plug & Chug d f =(0m)+(0m/s)(4.0s)+(9.8m/s 2 )(4.0s) 2 d f =78.4m Slide 19 A tennis ball is thrown straight up with an initial speed of 22.5m/s. It is caught at the same distance above the ground. How high does the ball rise? Define known & unknown: v i =22.5m/sv f =0m/s t=?g=-9.8m/s 2 d=? Choose the appropriate equation v f 2 =v i 2 +2g(d f -d i ) Rearrange if necessary d=(v f 2 -v i 2 )/(2g) Plug & Chug d=((0m/s) 2 -(22.5m/s) 2 )/(2(-9.8m/s 2 )) d=25.82m Slide 20 A tennis ball is thrown straight up with an initial speed of 22.5m/s. It is caught at the same distance above the ground. How long does the ball remain in the air? Define known & unknown: v i =22.5m/sv f =0m/s t=?g=-9.8m/s 2 d=25.82m Choose the appropriate equation v f =g t + v i Rearrange if necessary t=(v f -v i )/g Plug & Chug t=(0m/s-22.5m/s)/(-9.8m/s 2 ) t=2.30s Slide 21 As an objects speed approaches 3.0x10 8 m/s (c), the time as observed from the outside of the ship changes So if you are travelling very fast,