Question

a particle is moving along a straight line along y axis . at time t its position from origin is y=5t²-10t+5. where y in meter and t in second. what is the velocity at t=2 seconds? what is the magnitude of displacement of particle when its velocity is zero ? what is the average velocity for time interval 0<=t<=10s ?
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Answer 1

The correct question may be like:

a particle is moving along a straight line along y axis . at time t its position from origin is y=5t²-10t+5. where y in meter and t in second. what is the velocity at t=2 seconds? what is the magnitude of displacement of particle when its velocity is zero ? what is the average velocity for time interval 0<=t<=10s ? ​

• "The velocity of the particle at t=2 seconds is 20 m/s. The magnitude of displacement of the particle when its velocity is zero is 5 meters. The average velocity for the time interval 0<=t<=10s is 45 m/s.
• To find the velocity at t=2 seconds, we need to differentiate the given equation with respect to time. The derivative of y=5t²-10t+5 is dy/dt=10t-10. Substituting t=2, we get dy/dt=10(2)-10=20 m/s.
• To find the magnitude of displacement when the velocity is zero, we need to find the time at which the velocity becomes zero. Setting dy/dt=0, we get 10t-10=0, which gives t=1 second. Substituting t=1 in the given equation, we get y=5(1)²-10(1)+5=0. Hence, the particle is at the origin when its velocity is zero. Therefore, the magnitude of displacement is 5 meters.
• To find the average velocity for the time interval 0<=t<=10s, we need to find the total displacement and divide it by the total time taken. The displacement at t=10 is y=5(10)²-10(10)+5=445 meters. The displacement at t=0 is y=5(0)²-10(0)+5=5 meters. Therefore, the total displacement is 445-5=440 meters. The total time taken is 10-0=10 seconds. Hence, the average velocity is 440/10=45 m/s."

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