Question

A car rolling down a hill accelerates from rest to 22m/s in 40s. What is the average velocity of the car? What is the displacement of the car as it rolls down the hill?

Answer 1

`v_("average")= 11ms^(-1)`

`d= 440m`

Explanation:

The car is rolling down a hill so the acceleration is constant.
This is because acceleration due to gravity is constant, so the acceleration of the car on a given slope will be constant (assuming the slope of the hill is constant and ignoring friction).

equations we know:

1. `v_("average")=(Delta d)/ (Delta t)`
2. `v_("average")= (v_1-v_0)/2` (where `a` is constant)
3. `a_("average")=(Delta v)/ (Delta t)`
4. `d=v_("average")*t`
5. `d=v_0 t+1/2at^2` (where `a` is constant)
6. `Delta v = (v_1-v_0) = 22-0 = 22ms^(-1)`
7. `Delta t =40s`

we know that the car accelerates from `0 to 22ms^(-1)` in 40s so choosing eqn2 and eqn4. :

`v_("average")= (22-0)/2 = 11ms^(-1)`

`d=11ms^(-1)*40s = 440m`