A person travels a distance x = 20t+2At2, where A is a constant. The acceleration of the person is:
Correct answer: D. 4A ms^-2
- A. A/4 ms^-2
- B. 4/A ms^-2
- C. 4 ms^-2
- D. 4A ms^-2
Explanation
The given equation for distance is x = 20t + 2At^2. To find acceleration, we need to differentiate this equation with respect to time.First, differentiate to find velocity (v):v = dx/dt = d(20t + 2At^2)/dt = 20 + 4At.Then, differentiate the velocity to find acceleration (a):a = dv/dt = d(20 + 4At)/dt = 4A.Therefore, the acceleration of the person is 4A.The other options are incorrect as they either misinterpret the role of the constant A or incorrectly calculate the differentiation process.
This question appeared on the ETEA MDCAT 2012 paper, which you can sit online with every answer explained.
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About Acceleration
Acceleration measures the rate at which velocity changes with time, including changes in speed, direction or both. Work includes average and instantaneous acceleration, the relation a = Δv/Δt, uniform acceleration equations, and interpreting velocity time and displacement time graphs, with acceleration carefully distinguished from velocity.
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