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The acceleration of a particle increases linearly with time t as 6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in time t will be
- a)t
- b)t2
- c)t3
- d)t4
Correct answer is option 'C'. Can you explain this answer?
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The acceleration of a particle increases linearly with timet as6t. If ...
Explanation:
Given:
- Acceleration of the particle: a(t) = 6t
- Initial velocity of the particle: 0
- Particle starts from the origin
Using kinematic equations:
- We know that acceleration is the derivative of velocity with respect to time, which means:
a(t) = dv/dt
- Integrating both sides with respect to time, we get:
∫a(t) dt = ∫dv
- Integrating the given acceleration function, we get:
∫6t dt = v
v = 3t^2
- Since the initial velocity is 0, we have v(0) = 0, which means the velocity function is:
v(t) = 3t^2
- Distance travelled by the particle is the integral of velocity with respect to time:
∫v(t) dt = ∫3t^2 dt
∫3t^2 dt = t^3
Therefore, the distance travelled by the particle in time t is t^3, which corresponds to option 'c'.
Given:
- Acceleration of the particle: a(t) = 6t
- Initial velocity of the particle: 0
- Particle starts from the origin
Using kinematic equations:
- We know that acceleration is the derivative of velocity with respect to time, which means:
a(t) = dv/dt
- Integrating both sides with respect to time, we get:
∫a(t) dt = ∫dv
- Integrating the given acceleration function, we get:
∫6t dt = v
v = 3t^2
- Since the initial velocity is 0, we have v(0) = 0, which means the velocity function is:
v(t) = 3t^2
- Distance travelled by the particle is the integral of velocity with respect to time:
∫v(t) dt = ∫3t^2 dt
∫3t^2 dt = t^3
Therefore, the distance travelled by the particle in time t is t^3, which corresponds to option 'c'.
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The acceleration of a particle increases linearly with timet as6t. If the initial velocity of the particle is zero and the particle starts from the origin, then the distance travelled by the particle in timet will bea)tb)t2c)t3d)t4Correct answer is option 'C'. Can you explain this answer?
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