Question

A motorcycle moving with a speed of $5\,m{s^{ - 1}}$ is subjected to an acceleration of $0.2\,m{s^{ - 2}}$ . Calculate the speed of the motorcycle after $10\,s$ and also the distance travelled in this time.

Answer 1

Hint: Use the first equation of motion and substitute the known parameters to find the value of the final velocity of the motorcycle. Substitute this value in the second equation of motion, to find the value of the distance travelled by the motorcycle.

Formula used:
The formula of the equations of the motion is given by
$
  v = u + at \\
  {v^2} = {u^2} + 2as \\
 $
Where $v$ is the final velocity of the motorcycle, $u$ is the initial velocity of the cycle, $s$ is the displacement of the motorcycle, $a$ is the acceleration of the motorcycle and $t$ is the time taken for the travel.

Complete answer:
It is given that the
Speed of the motorcycle, $u = 5\,m{s^{ - 1}}$
Acceleration of the motorcycle, $a = 0.2\,m{s^{ - 2}}$
The time taken for the travel by the motorcycle, $t = 10\,s$
Use the first equation of the motion,
$v = u + at$
Substituting the values of the initial velocity of the motorcycle, acceleration and the time taken in the above equation, we get
$
  v = 5 + 0.2 \times 10 \\
  v = 7\,m{s^{ - 1}} \\
 $
Hence the final velocity of the motorcycle after $10$ seconds is obtained as $7\,m{s^{ - 1}}$ .
Using the other equation of motion,
${v^2} = {u^2} + 2as$
Substituting all the known parameters in it, we get
$
  {7^2} = {5^2} + 2 \times 0.2s \\
  49 = 25 + 0.4s \\
 $
By performing various arithmetic operations, we get
$s = 60\,m$
Hence the distance travelled by the motor cycle in time is obtained as $60\,m$ .

Note:
The final velocity of the motorcycle is greater than the initial velocity of it. Thus the motorcycle moves faster with the positive acceleration in the direction of the motorcycle. Remember the equations of motions since they are used in many problems and rea life applications.