Question

A ball rolls down an incline 12 m long in 3.0 s.

a. assuming that the ball is uniformly accelerated, what is its average speed?
b. what is its final speed? 2. a ball rolls down a hill with a constant acceleration of 3.0 m/s^2.
a. if it starts from rest, what is its speed at the end of 4.0 s?
b. how far did it move? 3. a car starting from rest is accelerated at the constant rate of 3.0 m/s^2.
a. what is its speed at the end of 8.0 s ?
b. how far did it travel during the first 8.0 s?

Answer 1

*note: initial speed is 0 when starting from rest*

1A)
Average speed = total distance / total time
= 12/3
= 4 m/s
1B)
average speed = (initial speed + final speed)/2
4 = (0 + v)/2
v = 8 m/s

2A)
Using
v = u + at, where v is the final speed, u is the initial speed (0 m/s), a is the acceleration (3 m/s²) and t is the time (4 s)
v = 0 + (3)(4)
v = 12 m/s
2B)
using
s = ut +0.5at² with u = 0,
s = 0.5(3)(4)²
s = 24 m

3A)
using
v = u + at, with u = 0
v = 0 + (3)(8)
v = 24 m/s
3B)
s = ut +0.5at²
s = 0.5(3)(8)²
s = 96 m