Question

give answer with explanation

Answer 1

The area under the curve/line in a graph of Velocity Vs Time gives the distance covered by the object. When the area is above X axis, it is positive, and when it's below X axis, it is negative.

So you can see can that when area is positive, particle moves forward and when area is negative, particle moves backward.

A particle speeds up if it's acceleration acceleration and velocity have both the same signs and when both of them have different signs, the particle slows down.

Now, acceleration of the particle in such a graph as given is given by the slope of the graph. If slope is negative, acceleration is also negative and if slope is positive, acceleration is also positive.

So according to what I just explained above, we will now answer the questions.

a) The particle moves forward when area is positive, that is the interval of 0-1 seconds and 5-7 seconds. The particle moves backward when area is negative, that is the interval of 2-5 seconds and 7-9... seconds. The particle speeds up when velocity and acceleration have same signs that is in the interval of 1-2 seconds and 5-6 seconds. It slows down in 0-1 seconds, 3-5 seconds and 6-7 seconds.

b) Acceleration is positive in the interval 3-6 seconds. Acceleration is negative in the interval 0-2 and 6-7 seconds. Acceleration is zero in the interval 2-3 seconds and 7-9... seconds.

c) The particle is at its greatest speed at 0 seconds and the interval 2-3 seconds and the greatest speed is 4 m/s since speed is magnitude, where 4 and -4 are same.

d) The particle stands still for more than an instant when the velocity is zero and acceleration is also zero. That happens in the interval 7-9... seconds