Question

A particle is moving in a straight line such that its velocity is increasing at $5 \,ms ^{-1}$ per meter. The acceleration of the particle is _____$ms ^{-2}$ at a point where its velocity is $20 \,ms ^{-1}$

Answer 1

Correct Answer: 100

To solve the problem, we need to find the particle's acceleration. We start with the information given: the rate of change of velocity with respect to distance is \( \frac{dv}{ds} = 5 \, ms^{-1} \, m^{-1} \). We are also given the velocity \( v = 20 \, ms^{-1} \).
Since acceleration \( a \) is the rate of change of velocity with respect to time, we can use the chain rule in calculus to express acceleration in terms of velocity and distance:

\[ a = v \frac{dv}{ds} \]
Substituting the known values into this equation:
\[ a = 20 \cdot 5 \]
\[ a = 100 \, ms^{-2} \]
This calculated acceleration of \( 100 \, ms^{-2} \) is verified to fall within the expected range of 100–100.
Therefore, the acceleration of the particle is \( 100 \, ms^{-2} \).