Question

A motorcycle moving at a constant velocity suddenly accelerates at a rate of 4.0 m/s² to a speed of 35 m/s in 5.0 s. What was the initial speed of the motorcycle?

a) (v_{{initial}} = 15 , {m/s})
b) (v_{{initial}} = 20 , {m/s})
c) (v_{{initial}} = 25 , {m/s})
d) (v_{{initial}} = 30 , {m/s})

Answer 1

The initial speed of the motorcycle was 15 m/s, calculated by rearranging the formula for acceleration and substituting the given values.

Step-by-step explanation:

To find the initial speed of the motorcycle, we can use the formula for acceleration: \(v_{final} = v_{initial} + a \times t\). Given that the motorcycle accelerates at a rate of 4.0 m/s², reaches a speed of 35 m/s in 5.0 s, we can rearrange the formula to solve for \(v_{initial}\):

\(v_{initial} = v_{final} - a \times t\)

Plugging in the values provided gives us:

\(v_{initial} = 35 m/s - (4.0 m/s² \times 5.0 s)\)

\(v_{initial} = 35 m/s - 20 m/s\)

\(v_{initial} = 15 m/s\)

This calculation shows that the initial speed of the motorcycle was 15 m/s, which corresponds to option a).