Question

The velocity of a body in motion in straight line with the uniform acceleration is given as v = 2t - 5. The net magnitude of displacement made by the body from t = 0  to t = 3 is 
1. 6 m
2. 3 m
3. 5 m
4. 2 m

Answer 1

Correct Answer - Option 1 : 6 m

Concept:

Displacement: The net change in position is called displacement. 

Velocity: It the rate of change of displacement. 

\(v = \frac{dx}{dt}\)

Writing this equation in another way. 

dx = v.dt

And if do integration both side, we will get

\(\int dx =\int_{t_1}^{t_2} v.dt\)

Calculation:

Given velocity v = 2t - 5

So, the displacement from t = 0 to t = 3 second is given as

\(x =\int_{0}^{3} (2t -5).dt\)

⇒ \(x = \left [ 2\frac{t^2}{2} \right ]_{0}^{3} - \left [ 5t \right ]_{0}^{3}\)

⇒ x = 3 ² - 5 × 3 = - 6 m

So, displacement is - 6 m

The magnitude of displacement is 6 m.