Question

Suppose a treadmill has an average acceleration of $4.7\times {{10}^{-3}}m/{{s}^{2}}$. How much does the speed change after 5 min? If the treadmill’s initial speed is $1.7m/s$, what will its final speed be?

Answer 1

Hint: We know that the formula for acceleration is equal to \[a=\dfrac{\Delta v}{\Delta t}\] . Now, in the above problem, we have given the value of acceleration and time and asked to find the change in velocity so we are going to put acceleration and time in the above formula and from that we will get the change in velocity. Also, we are asked to find the final speed and have given the initial speed. Change in velocity we have already calculated. Change is equal to the subtraction of initial speed from the final speed so using this relation we can find the final speed.

Complete step by step answer:
In the above problem, we have given treadmill’s acceleration of $4.7\times {{10}^{-3}}m/{{s}^{2}}$ and we are asked to find the change in speed after 5 min. For that, we are going to use the following formula:
\[a=\dfrac{\Delta v}{\Delta t}\] …….. Eq. (1)
Now, time is given in minutes so we are going to convert this time in seconds to keep the units in synchronization. Multiplying 5 minutes by 60 we get,
$\begin{align}
  & 5\times 60 \\
 & =300\sec \\
\end{align}$
Substituting the value of $\Delta t$ as 300 seconds and $a=4.7\times {{10}^{-3}}$ in eq. (1) we get,
\[4.7\times {{10}^{-3}}=\dfrac{\Delta v}{300}\]
Cross multiplying the above equation we get,
$\begin{align}
  & 4.7\times {{10}^{-3}}\times 300=\Delta v \\
 & \Rightarrow 14.1\times {{10}^{-1}}m/s=\Delta v \\
\end{align}$
Now, multiplying the L.H.S of the above equation we get,
$1.41m/s=\Delta v$
From the above, we have calculated the change in speed after 5 min is $1.41m/s$.
We have given the treadmill’s initial speed as $1.7m/s$and we are asked to find the final speed.
Change in speed is equal to the subtraction of initial speed from the final speed.
$\text{Change in Speed}=\left( \text{Final Speed} \right)-\left( \text{Initial Speed} \right)$
Substituting initial speed as $1.7m/s$ and change in speed as $1.41m/s$ in the above equation we get,
$\begin{align}
  & 1.41=\left( \text{Final Speed} \right)-1.7 \\
 & \Rightarrow 1.41+1.7=\text{Final Speed} \\
 & \Rightarrow \text{3}\text{.11m/s}=\text{Final Speed} \\
\end{align}$

From the above, we have calculated the final speed as 3.11 m/s.

Note: The plausible mistake that could happen in the above problem is that you might forget to convert the time into seconds. So, make sure you will convert the time in minutes into seconds so that the units of acceleration and the expression on the right hand side of the above equation will be correctly matched.
\[a=\dfrac{\Delta v}{\Delta t}\]