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A particle moves along a straight line p...

A particle moves along a straight line path. After some time it comes to rest. The motion is with constant acceleration whose direction with respect to the direction of velocity is :

A

positive throughout motion

B

negative throughout motion

C

first positive then negative

D

first negative then positive

Text Solution

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The correct Answer is:
To solve the question, we need to analyze the motion of a particle that comes to rest under constant acceleration. Here’s a step-by-step breakdown of the solution: ### Step 1: Understand the Problem We have a particle moving along a straight line, initially with some velocity \( u \). The particle eventually comes to rest, meaning its final velocity \( v = 0 \). ### Step 2: Identify the Variables - Initial velocity: \( u \) - Final velocity: \( v = 0 \) - Acceleration: \( a \) (unknown) - Time: \( t \) (unknown) ### Step 3: Use the Kinematic Equation We can use the kinematic equation that relates initial velocity, final velocity, acceleration, and time: \[ v = u + at \] Substituting \( v = 0 \): \[ 0 = u + at \] ### Step 4: Rearrange the Equation Rearranging the equation gives: \[ at = -u \] This implies: \[ a = -\frac{u}{t} \] ### Step 5: Analyze the Signs Since \( t \) (time) is always positive, the sign of \( a \) depends on the sign of \( u \): - If \( u \) is positive (the particle moves in the positive direction), then \( a \) must be negative to bring the particle to rest. - If \( u \) is negative (the particle moves in the negative direction), then \( a \) must be positive to bring the particle to rest. ### Step 6: Conclusion on the Direction of Acceleration In both cases, the acceleration \( a \) is in the opposite direction to the initial velocity \( u \). Therefore, the direction of acceleration is negative with respect to the direction of velocity. ### Final Answer The direction of acceleration with respect to the direction of velocity is negative. ---
To solve the question, we need to analyze the motion of a particle that comes to rest under constant acceleration. Here’s a step-by-step breakdown of the solution: ### Step 1: Understand the Problem We have a particle moving along a straight line, initially with some velocity \( u \). The particle eventually comes to rest, meaning its final velocity \( v = 0 \). ### Step 2: Identify the Variables - Initial velocity: \( u \) - Final velocity: \( v = 0 \) ...
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