Question

In an experiment, students measure the position x of a cart as a function of time t for a cart that starts at rest and moves with a constant acceleration. The following data are collected for the cart.

t(s) x(m)
0 0
1 4
2 16
3 36
4 64

The acceleration of the cart is most nearly:_____

Answer 1

Given :

Initial velocity , u = 0 m/s² .

To Find :

The acceleration of the cart.

Solution :

Since, acceleration is constant.

Using equation of motion :

`x = ut + (at^2)/(2)\\\\x = (at^2)/(2)`

Putting, t = 1 s and x = 4 m in above equation, we get :

`4 = (a(1)^2)/(2)\\\\a = 8 \ m/s^2`

Therefore, the acceleration of the cart is 8 m/s².