Question

A cart rolls down a ramp with an acceleration of 4.2 m/sec^2. If the cart starts from rest, how fast is it moving at the end of 4 seconds?

Answer 1

A cart rolls down a ramp with an acceleration of $4.2 \, \text{m/sec}^2$. If the cart starts from rest, how fast is it moving at the end of 4 seconds?

Solution

We are given

$$a = 4.2 \, \frac{m}{s^2}$$ $$v_0 = 0 \text{ (the cart starts from rest)}$$ $$t = 4 \, s$$

Acceleration is uniform

(http://en.wikipedia.org/wiki/Acceleration#Uniform_acceleration)

So velocity depends on time as:

$$v(t) = v_0 + a * t$$

Velocity at the end of 4 seconds is:

$$v(4) = v_0 + a * 4 = 0 + 4.2 * 4 = 16.8 \, \text{m/s}$$

Answer:

$$v(4) = 16.8 \, \text{m/s}$$