A motorcycle moves along a straight road. Its velocity at each second is recorded as follows: at $t=0s$, $v=0m/s$; at $t=1s$, $v=2m/s$; at $t=2s$, $v=4m/s$; at $t=3s$, $v=4m/s$; at $t=4s$, $v=6m/s$. At which second does the motorcycle first start to have positive acceleration?

• A. At $2$ seconds
• B. At $1$ second
• C. At $3$ seconds
• D. At $4$ seconds

Answer: (B)

Verified step by step guidance

1. Recall that acceleration is defined as the rate of change of velocity with respect to time, mathematically given by \(a = \frac{\Delta v}{\Delta t}\).
2. Calculate the change in velocity between each consecutive second by subtracting the velocity at the previous second from the velocity at the current second.
3. For each time interval, compute the acceleration using \(a = \frac{v_{t} - v_{t-1}}{1\,\text{s}}\), since the velocity is recorded every 1 second.
4. Identify the first time interval where the acceleration value is positive, meaning the velocity is increasing during that interval.
5. The time at which the motorcycle first starts to have positive acceleration corresponds to the beginning of that interval (the earlier time).