Question

A bus traveling at 40 m/s accelerates at a constant rate of 3.5 m/s2 over a distance of 50 m. What is its speed after accelerating?

Answer 1

We know that

• The initial speed is 40 m/s.

,

• The acceleration is 3.5 m/s^2.

,

• The distance covered is 50 m.

Let's use the following formula to find the final speed.

`v^2_f=v^2_0+2ad`

Where V0 = 40 m/s, a = 3.5 m/s^2, and d = 50m.

`\begin{gathered} v^2_f=(40\cdot(m)/(s))^2+2(3.5\cdot(m)/(s^2))(50m) \\ v^2_f=1600\cdot(m^2)/(s^2)+350\cdot(m^2)/(s^2) \\ v^2_f=1950\cdot(m^2)/(s^2) \\ v_f=\sqrt[]{1950\cdot(m^2)/(s^2)} \\ v_f\approx44\cdot(m)/(s) \end{gathered}`

Therefore, the speed after accelerating is 44 m/s.