Question

The acceleration-time graph of a particle moving with initial velocity 20 m/s is shown below. The velocity of body at t = 20 s is​

Answer 1

Answer:

Explanation:6 m/s

Explanation:

The acceleration time graph a particle moving in a straight line is as shown in figure. The velocity of the particle at time t = 0 is 2 m/s. The velocity after 2 seconds will be

(B) 6 m/s

(a) 8m/s

(C) 4 m/s

(D 2 m/s

V = u + at

u = 2m/s

at = Area under graph

at = (1/2) (2) (4) = 4

V=2+4= 6 m/s

Answer 2

The velocity of the body after t = 20 s is 120 m/s.

Given:

The acceleration-time graph of a particle is given.

The initial velocity of the particle, u = 20 m/s.

The time for which velocity of the body is to be calculated, t = 20 s.

To Find:

We have to find the velocity of the given body having an initial velocity of 20 m/s after t = 20 s.

Solution:

The area under the given acceleration-time graph gives the change in velocity in a specific time interval.

The area under the given graph is a rectangle. Therefore, the equation for the area of a rectangle is given by,

Area of a rectangle, A = Length × Breadth.

From the graph, length of the rectangle = t = 20 s.

The breadth of the rectangle = 5 m/s².

∴, Area (A) = 20 × 5 = 100 m².

Given that the initial velocity of the particle is 20 m/s.

i.e., The change in the velocity = Initial velocity + Area under the given graph.

On substituting the given values in above equation, we get,

The change in the velocity = 20 + 100 = 120 m/s.

Hence, the velocity of the given body with initial velocity 20 m/s after t = 20 s is  120 m/s.

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