Question

A motorcycle moving with a speed of is subjected to an acceleration of $5\;{\text{m}}{{\text{s}}^{ - 1}}$Calculate the speed of the motorcycle after$10\;{\text{seconds}}$, and the distance travelled in this time.

Answer 1

Hint
The above problem can be solved by using the equation of the motions. There are three equations of motion. The speed, time acceleration and distance can easily be found by these three equations of motion.

Complete step by step answer
Given: The initial speed of the motorcycle is $u = 5\;{\text{m}}{{\text{s}}^{ - 1}}$, the time taken by the motorcycle is $t = 10\;{\text{s}}$, the acceleration of the motorcycle is $a = 2\;{\text{m}}{{\text{s}}^{ - 2}}$.
Write the first equation of motion to find the final speed of the motorcycle.
$\Rightarrow v = u + at......\left( 1 \right)$
Substitute $5\;{\text{m}}{{\text{s}}^{ - 1}}$for u, $10\;{\text{seconds}}$ for t and $\Rightarrow 2\;{\text{m}}{{\text{s}}^{ - 2}}$for a in the equation (1) to find the final speed of the motorcycle.
$\Rightarrow v = 5\;{\text{m}}{{\text{s}}^{ - 1}} + \left( {2\;{\text{m}}{{\text{s}}^{ - 2}}} \right)\left( {10\;{\text{seconds}}} \right)$
$\Rightarrow v = 25\;{\text{m}}{{\text{s}}^{ - 1}}$
Write the third equation of motion to find the distance travelled by the motorcycle.
$\Rightarrow {v^2} = {u^2} + 2as$
$\Rightarrow s = \dfrac{{{v^2} - {u^2}}}{{2a}}......\left( 2 \right)$
Substitute $5\;{\text{m}}{{\text{s}}^{ - 1}}$for u and $2\;{\text{m}}{{\text{s}}^{ - 2}}$for a in the equation (1) to find the distance travelled by the motorcycle.
$\Rightarrow s = \dfrac{{{{\left( {25\;{\text{m}}{{\text{s}}^{ - 1}}} \right)}^2} - {{\left( {5\;{\text{m}}{{\text{s}}^{ - 1}}} \right)}^2}}}{{2\left( {2\;{\text{m}}{{\text{s}}^{ - 2}}} \right)}}$
$s = 150\;{\text{m}}$
Thus, the final speed of the motorcycle is $25\;{\text{m}}{{\text{s}}^{ - 1}}$ and the distance travelled by the motorcycle is $150\;{\text{m}}$.

Additional Information
The speed of the particle is the same as the variation in the position of the particle with time and the acceleration is same as the consecutive variation in the position of the particle with time. The slope of the position- time graph describes the velocity and slope of the velocity-time graph describes the acceleration of the particle.

Note
The distance travelled by the motorcycle can also be found by using the second equation of motion and final speed of the motorcycle can be found by using the third equation of the motion.