Figure 3.25 gives a speed-time graph of a particle in motion along a constant direction. Three equal intervals of time are shown. In which interval is the average acceleration greatest in magnitude? In which interval is the average speed greatest? Choosing the positive direction as the constant direction of motion, give the signs of v and a in the three intervals. What are the accelerations at the points A, B, C and D?
We know that,
Slope of s-t graph represents acceleration.
y- Coordinate of point on s-t graph represents speed.
From the given s-t graph,
Slope is maximum in interval 2. So, it has maximum average acceleration.
y- Coordinate value of point in interval 3 has highest value thus, interval 3 has maximum average speed.
In interval 1,
Slope is positive. So, acceleration is positive.
y- Coordinate of points are positive. So, speed is positive.
In interval 2,
Slope is negative. So, acceleration is negative.
y- Coordinate of points are positive. So, speed is positive.
In interval 3,
Slope is positive. So, acceleration is positive.
y – Coordinate of points are positive. So, speed is positive.
At A, B and C slopes of curve are ‘0’. Thus, Acceleration at this point are zero.