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A particle's velocity is given by v(t) = 20t − 5t2. What is its acceleration?

May 14, 2026Physics

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Answer

\text{E) } 20 - 10t

Graph of v(t) = 20t − 5t²

4 steps

Identify the given velocity function.
The velocity of the particle is given by the function $v(t) = 20t - 5t^2$ .
Recall the relationship between velocity and acceleration.
Acceleration $a(t)$ is the first derivative of the velocity function $v(t)$ with respect to time $t$ .
$a(t) = \frac{dv}{dt}$
Differentiate the velocity function.
Differentiate $v(t) = 20t - 5t^2$ with respect to $t$ :
$a(t) = \frac{d}{dt}(20t - 5t^2)$ $a(t) = \frac{d}{dt}(20t) - \frac{d}{dt}(5t^2)$ $a(t) = 20(1) - 5(2t)$ $a(t) = 20 - 10t$
Compare the result with the given options.
The calculated acceleration is $a(t) = 20 - 10t$ . This matches option (E).

The final answer is $\text{E) } 20 - 10t$ .

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