Question:
The variation of speed (in m/s) of an object with time (in seconds) is given by the expression $V(t) = V_0 - 5t + 5t^2$
The variation of speed (in m/s) of an object with time (in seconds) is given by the expression $V(t) = V_0 - 5t + 5t^2$
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If the acceleration function $a(t)$ has a negative value at a given time, the object is decelerating at that moment.
Updated On: May 1, 2026
- At time $t = 0$ s, the instantaneous acceleration is zero
- At time $t = 0$ s, there is a deceleration of the object
- At time $t = 1$ s, the object is at rest
- At time $t = 1$ s, the instantaneous acceleration is zero
- The distance travelled by the object at time $t = 1$ s is $V_0$ m
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The Correct Option is B
Solution and Explanation
Concept:
Instantaneous acceleration ($a$) is defined as the rate of change of velocity with respect to time, which is the first derivative of the velocity function: \[ a(t) = \frac{dV}{dt} \]
Step 1: Differentiate the velocity function.
Given the function $V(t) = V_0 - 5t + 5t^2$: \[ a(t) = \frac{d}{dt}(V_0 - 5t + 5t^2) \] \[ a(t) = 0 - 5 + 10t = -5 + 10t \]
Step 2: Evaluate acceleration at $t = 0$.
\[ a(0) = -5 + 10(0) = -5 \text{ m/s}^2 \]
Step 3: Interpretation of the result.
A negative acceleration value at the start of motion ($t=0$) indicates that the object is experiencing a force opposite to its initial velocity direction, causing it to slow down. This is physically termed as deceleration.
Instantaneous acceleration ($a$) is defined as the rate of change of velocity with respect to time, which is the first derivative of the velocity function: \[ a(t) = \frac{dV}{dt} \]
Step 1: Differentiate the velocity function.
Given the function $V(t) = V_0 - 5t + 5t^2$: \[ a(t) = \frac{d}{dt}(V_0 - 5t + 5t^2) \] \[ a(t) = 0 - 5 + 10t = -5 + 10t \]
Step 2: Evaluate acceleration at $t = 0$.
\[ a(0) = -5 + 10(0) = -5 \text{ m/s}^2 \]
Step 3: Interpretation of the result.
A negative acceleration value at the start of motion ($t=0$) indicates that the object is experiencing a force opposite to its initial velocity direction, causing it to slow down. This is physically termed as deceleration.
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