## A few quick problems with kinematics

Hi there,

Sorry for so many questions, but I feel frankly stupid for getting these wrong, and yet I have no clue why they're so off. Any ideas of why the answers are what they are? Thanks so much.

15. A truck starts from rest and accelerates at 1.5 m/s2for 20 s. It then travels at constant speed for 20 s and decelerates at –1.5 m/s2until it stops. How far did the truck travel?

a. 300 m

b. 600 m

*c. 1200 m

d. 1500 m

I got 600 because I used x = 1/2at^2 + v0t + x0 with v0 = 0, a = 1.5 m/s^2, t = 20 s, and x = ?

17. A ball is dropped from the top of a tall building. Just before it strikes the ground it is moving at 34.3 m/s. How tall is the building?

a. 60 m

*b. 131 m

c. 250 m

d. 125 m

I got 60 m using v^2 = 2ax with v0 = 0, vf = 34.3 m/s, a = -9.8 m/s^2, and x = ?

18. A bus leaves a terminal en-route to a destination 200 km away. During the trip, the bus stopped for a 45 minute lunch. The bus arrived at its destination four hours after it departed. The average velocity was:

a. 0 km/hr

b. 61 km/hr

c. 30 km/hr

*d. 50 km/hr

I used v = (delta)x / (delta)t with delta x = 200 km, and delta t = 3.25 hr

19. The position of a particle is given by x ( t ) =24 t – 4 t 2. At what time is the particle at rest?

*a. 3s

b. 8s

c. 10s

d. 2s

I got 6, Wolfram got 6, I'm very confused.

20. The position of a particle as a function of time is given by 4 t +3 t 2–2 t 3. What is the average acceleration over the time interval from 0 to 4s?

a. 90 m/s2

*b. –18m/s2

c. –102 m/s2

d. 102 m/s2

Since acceleration is the second-derivative of position, I got 6 - 12t. Which apparently is wrong.

Thanks again.
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 Quote by m00nbeam360 15. A truck starts from rest and accelerates at 1.5 m/s2for 20 s. It then travels at constant speed for 20 s and decelerates at –1.5 m/s2until it stops. How far did the truck travel? a. 300 m b. 600 m *c. 1200 m d. 1500 m I got 600 because I used x = 1/2at^2 + v0t + x0 with v0 = 0, a = 1.5 m/s^2, t = 20 s, and x = ?
Did you include the constant speed segment? (I'd say that none of the answers are correct.)

 17. A ball is dropped from the top of a tall building. Just before it strikes the ground it is moving at 34.3 m/s. How tall is the building? a. 60 m *b. 131 m c. 250 m d. 125 m I got 60 m using v^2 = 2ax with v0 = 0, vf = 34.3 m/s, a = -9.8 m/s^2, and x = ?
Your answer is correct.

 18. A bus leaves a terminal en-route to a destination 200 km away. During the trip, the bus stopped for a 45 minute lunch. The bus arrived at its destination four hours after it departed. The average velocity was: a. 0 km/hr b. 61 km/hr c. 30 km/hr *d. 50 km/hr I used v = (delta)x / (delta)t with delta x = 200 km, and delta t = 3.25 hr
The zero-speed segment counts. Δt = 4 hours.
 19. The position of a particle is given by x ( t ) =24 t – 4 t 2. At what time is the particle at rest? *a. 3s b. 8s c. 10s d. 2s I got 6, Wolfram got 6, I'm very confused.
The speed is zero, not the position.

 20. The position of a particle as a function of time is given by 4 t +3 t 2–2 t 3. What is the average acceleration over the time interval from 0 to 4s? a. 90 m/s2 *b. –18m/s2 c. –102 m/s2 d. 102 m/s2 Since acceleration is the second-derivative of position, I got 6 - 12t. Which apparently is wrong.
They want the average acceleration, not the instantaneous acceleration.

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