Assertion (A): For uniformly accelerated motion along straight line, the position versus time graph is a straight line.
Reason (R): For uniformly accelerated motion the position in equal intervals of time changes by same amount.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is false.
For uniformly accelerated motion, position \( x \) is related to time \( t \) by \( x = x_0 + v_0 t + \frac{1}{2} a t^2 \). This is a parabolic equation, so the position-time graph is a parabola, not a straight line.
Reason (R) is false. In uniformly accelerated motion, velocity changes by equal amounts in equal time intervals, but position does not. Position changes by increasing amounts (if starting from rest).
Therefore, both the Assertion and the Reason are false.
Assertion (A): In one dimensional motion, area under velocity-time graph gives change in position i.e., displacement.
Reason (R): In one dimensional motion, area under acceleration-time graph gives final velocity.
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
Area under v-t graph = displacement; Area under a-t graph = change in velocity.
Solution: (A) is true as area under v-t graph is displacement. (R) is false as area under a-t graph gives change in velocity, not final velocity. So, (A) is true and (R) is false.
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.