The velocity of a particle is v=(2t^2-4t 3) m/s where t is tha time in second .find tha acceleration of this particle at t=2 seconds.?

Question

Answer

A=(4*2)-4= 4m/s^2

Answer

Given:

The velocity of a particle is given by the equation v = 2t^2 - 4t + 3 m/s, where t is the time in seconds.

To Find:

The acceleration of the particle at t = 2 seconds.

Explanation:

To find the acceleration, we need to differentiate the velocity function with respect to time. The derivative of velocity with respect to time gives us the acceleration.

Given, v = 2t^2 - 4t + 3 m/s

Differentiating both sides of the equation with respect to time (t), we get:

dv/dt = d/dt (2t^2 - 4t + 3)

Derivation:

Using the power rule of differentiation, we differentiate each term separately:

d/dt (2t^2) = 2 * 2t^1 = 4t
d/dt (-4t) = -4
d/dt (3) = 0

Therefore, dv/dt = 4t - 4

Substituting t = 2:

To find the acceleration at t = 2 seconds, we substitute t = 2 into the equation dv/dt = 4t - 4:

dv/dt = 4t - 4
dv/dt = 4(2) - 4
dv/dt = 8 - 4
dv/dt = 4 m/s^2

Therefore, the acceleration of the particle at t = 2 seconds is 4 m/s^2.

Conclusion:

The acceleration of the particle at t = 2 seconds is 4 m/s^2. This means that the rate of change of velocity with respect to time at t = 2 is 4 m/s^2.

Similar NEET Doubts

The acceleration 'a' in m/s² of a particle is given by a=3t^2 2t 2 where t is the time. If the particle starts out with a velocity, u=2m/s at t=0, then the velocity at the end of 2 seconds will be?

The acceleration 'a' in m/s² of a particle is given by a = 3t^2 2t 2 where t is the time. If the particle starts out with a velocity. u = 2 m/s at t=0, then the velocity at the end of 2 seconds will be?

A particle having initial velocity u moves with constant acceleration a for a time t . (

The position of a particle moving in the xy-plane at any time t is given by x = (3t2-6t) metres, y = (t2-2t) metres. Select the correct statement about the moving particle from the following

A particle is given velocity 3m/s along the positive x-axis subjected to a constant acceleration 4m/s along the positively y-axis. find the displacement of the particle in 2 seconds?

Top Courses for NEETView all

Biology Class 11

Daily Test for NEET Preparation

NEET Mock Test Series 2025

Topic-wise MCQ Tests for NEET

Physics Class 11

Top Courses for NEET

Top Courses for NEET

Suggested Free Tests

Related Content

About NEET

NEET Preparation Material

How to Prepare for NEET Exam?

NCERT Based Study Material

NEET Mock Tests

Other Popular Exams

Company