Question

The following figure gives the movement of an object. Select the correct statement from the given choices

• A. The total distance travelled by the object is $975$ m
• B. The maximum acceleration of the object is $2 \text{ m/s}^2$
• C. The maximum deceleration happened between $25^{\text{th}}$ and $35^{\text{th}}$ seconds
• D. The object was at rest between $10^{\text{th}}$ and $15^{\text{th}}$ seconds
• E. At $40^{\text{th}}$ second, the object was decelerating

Hint:

In speed-time graphs, steepest downward slope represents maximum deceleration, while flat lines indicate zero acceleration.

Answer 1

The Correct Option is C

Concept:
From a speed-time graph:
• Slope gives acceleration.
• Area under the curve gives distance.
• Horizontal line indicates constant speed (zero acceleration).

Step 1: Check acceleration and deceleration.
Between $25$ s and $35$ s, speed decreases from $40$ m/s to $20$ m/s: \[ a = \frac{20 - 40}{10} = -2 \text{ m/s}^2 \] This is the largest negative slope (maximum deceleration).

Step 2: Check other options.
- From $0$ to $10$ s, acceleration = $\frac{15-0}{10} = 1.5$ m/s$^2$ (not maximum).
- From $15$ to $25$ s, acceleration = $\frac{40-15}{10} = 2.5$ m/s$^2$ (maximum positive acceleration, so option B is false).
- From $10$ to $15$ s, speed is constant (not zero), so object is not at rest.
- At $40$ s, graph is horizontal → no acceleration. \[ \Rightarrow \text{Correct statement is (C)} \]