Kinematics Review

 

1.              Joe can run at 7.0 m/s. Sheila can run at 4.0 m/s. Joe gives Sheila a 40 m head-start. Using a distance vs time graph...

 

 

a)   Determine how long it takes Joe to catch Sheila. 13.3 s

b)   Determine how far Joe travels by the time he catches Sheila. 93.3 m

c)   At what time will Joe be 10 m ahead of Sheila? 16.7 s

d)   When Joe has run 200 m, how far has Sheila run? 154.3 m

e)     Write equations for JoeÕs motion and SheilaÕs motion. Joe   d + 40 = 7.0 t;  Sheila  d = 4.0 t  OR  Joe   d = 7.0 t;  Sheila  d = 4.0 t + 40

 

2.     A motorcyclist accelerates from 3.0 m/s to 27 m/s in 4.0 s. What is his acceleration? 6.0 m/s2

 

3.     A car accelerates at 5.0 m/s2 from an initial velocity of 14 m/s. How long will it take to reach a velocity of 65 m/s? 10.2 s

 

4.     A car accelerates form rest at 12.0 m/s2 for 14.0 s.

a)  How fast is it moving after 14.0 s? 168 m/s

b) How far has it traveled in this time? 1176 m = 1180 m

 

5.     A skier accelerates down a slope with an acceleration of 4.2 m/s2. She passes the first timing gate at 18 m/s. 6.0 s later she passed a second timing gate.

a)  How fast is she going as she passes the second gate? 43.2 m/s

b) What is the distance between the gates? 184 m/s

 

6.                                   Velocity vs. time                                                Displacement vs.  time

              

 

a)     Find the acceleration of the object. Slope is acceleration = 0.67 m/s2

b)    Write the equation for the graph. v = 0.67 t - 4

c)     Verify that your equation is correct by showing a ÒcheckÓ, i.e. pick a point on the line, take its value for t and see if you get the appropriate value for v (or vice versa). t = 12 s gives v = 4.0 m/s

d)    From the graph determine the DISTANCE traveled by the object in 15 seconds. Add areas d = 39 m

e)     From the graph determine the DISPLACEMENT of the object at 15 seconds. Add areas d = 15 m

f)     Verify the displacement from the graph by using the appropriate equation and show your calculation for displacement. v = 0.67 t - 4

 

7.     A motorcyclist starting from rest averages 24 m/s along a 500 m track. What was his acceleration? (Assume constant acceleration) 2.3 m/s2

 

8.     A block of wood was sliding along on level ice. Its initial speed was 18 m/s. If it took 15 seconds to come to a complete stop, what was the acceleration due to friction? Ð1.2 m/s2

 

9.     An object is dropped from rest near the surface of the Moon. The acceleration due to gravity on the Moon is 1.67 m/s2. What is the speed of the object after it has dropped 54 m? 13.4 m/s

 

10.  A skier passes a photogate traveling at 12 m/s. 30 m further down the slope she passes another photogate and is found to be traveling at 18 m/s. Assuming a constant slope what is the skier's acceleration? 3.0 m/s2

 

11.  An astronaut jumps off a 3.0 m ledge on the moon. What is the astronaut's speed as he hits the ground? 3.17 m/s What would be the final speed of someone jumping off a similar ledge on earth? 7.67 m/s (Assume negligible friction).

 

12.  A ball is thrown vertically upwards at an initial speed of 26 m/s. The acceleration due to gravity is -9.8 m/s2 (downwards!). How long will the ball take to reach its maximum height? 2.65 s What is its maximum height? 34.5 m

 

13.  An object is thrown vertically upwards at 24 m/s. The acceleration due to gravity is 9.8 m/s2.

 

a)         Draw a velocity vs time graph representing the objects motion.

 

b)             How high will the object be after 2.0 s? 28.4 m

c)              How fast will the object be traveling after 2.0 s? 4.4 m/s

d)             How long will it take for the object to reach its maximum height? (Hint: what do you know about the velocity of an object at its maximum height?) 2.45 s

e)              What is the objectÕs maximum height? 29.4 m