Assertion (A): For motion from rest with constant acceleration distance time graph is a parabola, always with increasing slope.
Reason (R): Speed of the body starting from rest with constant acceleration always increases linearly with time.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Formula: For (u=0), \(s = \frac{1}{2}at^2\) and (v = at).
Solution: (A) is true; \(s = \frac{1}{2}at^2\) is a parabola, and its slope (velocity (v=at)) increases with time. (R) is true; (v=at) shows speed increases linearly from rest. (R) correctly explains (A) because the linearly increasing speed implies an increasing slope for the distance-time graph.
Assertion (A): Trajectory of an object moving under a constant acceleration must be a straight line.
Reason (R): The shape of trajectory depends only on the acceleration.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is false; under constant acceleration, the trajectory can be a parabola (projectile motion) or a straight line depending on initial velocity. Reason (R) is false; the trajectory's shape depends on both initial velocity and acceleration.