In this question, all lengths are in metres and time, , is in seconds.
The diagram shows the displacement–time graph for a runner, for .
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In this question, all lengths are in metres and time, , is in seconds.
The diagram shows the displacement–time graph for a runner, for .
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A particle travels in a straight line. As it passes through a fixed point , the particle is travelling at a velocity of . The particle continues at this velocity for 60 seconds then decelerates at a constant rate for 15 seconds to a velocity of . The particle then decelerates again at a constant rate for 5 seconds to reach point , where it stops.
Sketch the velocity-time graph for this journey on the axes below.
Find the distance between and .
Find the deceleration in the last 5 seconds.
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The diagram shows the graph for a runner, where displacement, , is measured in metres and time, , is measured in seconds.
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A particle moves in a straight line such that its displacement, , from a fixed point at time is given by .
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In this question, the units are metres and seconds.
A particle is travelling in a straight line. Its acceleration, , away from a fixed point , at time , is given by , where .
When, is travelling with a velocity of 8 and has a displacement of from .
Find an expression for the velocity of at time .
Explain why is never at rest.
Find the displacement of from when .
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A particle, , moves in a straight line such that its displacement from a fixed point at time is s.
The acceleration of is given by
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At time , a particle travelling in a straight line has acceleration . When , the particle is from a fixed point and is travelling with velocity away from .
Find the velocity of the particle at time .
Find the displacement of the particle from at time .
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The diagram shows the velocity–time graph for a particle travelling in a straight line with velocity at time . The particle accelerates at for the first 10 s of its motion and then travels at constant velocity, , for . The particle then decelerates at a constant rate and comes to rest. The distance travelled during the interval .
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The diagram shows the velocity–time graph of a particle that travels 2775 m in 90 s, reaching a final velocity of .
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The displacement,, of a particle from a fixed point at time is given by .
Find the acceleration of the particle when .
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A particle moves in a straight line such that, seconds after passing through a fixed point , its acceleration, , is given by . When , the velocity of is .
Find the time at which comes to instantaneous rest.
Find the distance travelled by in the 3rd second.
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The acceleration, , of a particle travelling in a straight line, is given by at time . When the particle is at point and is travelling with a velocity of .
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A particle moves in a straight line such that, seconds after passing a fixed point , its displacement from is , where .
Find expressions for the velocity and acceleration at time .
Find the time when the particle is instantaneously at rest.
Find the acceleration at this time.
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