Question:
The velocity-time graph of a particle is given by \(v=4t\). The acceleration is:
The velocity-time graph of a particle is given by \(v=4t\). The acceleration is:
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If velocity is given as a function of time, acceleration is found by differentiating velocity with respect to time.
Updated On: Jun 3, 2026
- \(2\ \text{m/s}^2\)
- \(4\ \text{m/s}^2\)
- \(8\ \text{m/s}^2\)
- Variable
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The Correct Option is B
Solution and Explanation
Concept:
Acceleration is the rate of change of velocity with respect to time. So, \(\displaystyle a=\frac{dv}{dt}\)
Step 1: Write the given velocity equation.
\(\displaystyle v=4t\)
Step 2: Differentiate velocity with respect to time.
\(\displaystyle a=\frac{dv}{dt}\) \(\displaystyle a=\frac{d}{dt}(4t)\) \(\displaystyle a=4\)
Step 3: Write the unit.
Acceleration is measured in: \(\displaystyle \text{m/s}^2\) So, \(\displaystyle a=4\ \text{m/s}^2\)
Step 4: Final conclusion.
Hence, the acceleration is: \(\displaystyle \boxed{4\ \text{m/s}^2}\)
Acceleration is the rate of change of velocity with respect to time. So, \(\displaystyle a=\frac{dv}{dt}\)
Step 1: Write the given velocity equation.
\(\displaystyle v=4t\)
Step 2: Differentiate velocity with respect to time.
\(\displaystyle a=\frac{dv}{dt}\) \(\displaystyle a=\frac{d}{dt}(4t)\) \(\displaystyle a=4\)
Step 3: Write the unit.
Acceleration is measured in: \(\displaystyle \text{m/s}^2\) So, \(\displaystyle a=4\ \text{m/s}^2\)
Step 4: Final conclusion.
Hence, the acceleration is: \(\displaystyle \boxed{4\ \text{m/s}^2}\)
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