Question

Compare the acceleration of a motorcycle that accelerates from 80 km/h to 90 km/h with the acceleration of a bicycle that accelerates from rest to 10 km/h in the same time.

Short answer

The acceleration of both the motorcycle and the bicycle is the same.

Step-by-step solution

Step 1. Expression for acceleration

An object’s acceleration can be calculated by evaluating its initial and final velocities. Acceleration is inversely related to the time in which the object completes its movement.

Step 2. Identifying the given information

Given data:

The initial velocity of the motorcycle,$v_{i,m}=80\frac{\mathrm{km}}{\mathrm{h}}$

The final velocity of the motorcycle,$v_{f.m}=90\frac{\mathrm{km}}{\mathrm{h}}$

The final velocity of the bicycle,$v_{f,b}=10\frac{\mathrm{km}}{\mathrm{h}}$

As the bicycle accelerates from rest,

The initial velocity of the bicycle,$v_{i.b}=0$

Let $t$be the elapsed time for both the motorcycle and the bicycle.

Step 3. Calculation of the acceleration of the motorcycle

The acceleration of the motorcycle can be calculated as:

$\begin{array}{c}{a}_m=\frac{v_{f.m}-v_{i,m}}{t}\\ a_m=\frac{\left(90\frac{\mathrm{km}}{\mathrm{h}}\right)-\left(80\frac{\mathrm{km}}{\mathrm{h}}\right)}{t}\\ a_m=\frac{\left(10\frac{\mathrm{km}}{\mathrm{h}}\right)}{t}\dots \left(i\right)\end{array}$

Step 4. Calculation of the acceleration of the bicycle

The acceleration of the bicycle can be calculated as:

$\begin{array}{c}{a}_b=\frac{v_{f.b}-v_{i,b}}{t}\\ a_b=\frac{\left(10\frac{\mathrm{km}}{\mathrm{h}}\right)-\left(0\frac{\mathrm{km}}{\mathrm{h}}\right)}{t}\\ a_b=\frac{\left(10\frac{\mathrm{km}}{\mathrm{h}}\right)}{t}\dots \left(ii\right)\end{array}$

From equations (i) and (ii), the acceleration of both the motorcycle and the bicycle is the same.