Mechanics/Kinematic Calculus

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A particle P moves on the x-axis. At time t seconds the velocity of P is V m/s in the direction of x increasing?o
V is given by V={8t-3/2t²} for 0≤t≤4
Also V={16-2t} for t>4

Why does the acceleration have to equal zero to get the greatest speed of P in interval 0≤t≤4
 

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  • #2
Dale
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This is probably best understood by plotting the velocity. Look at the maximum, and see what the slope is visually.
 
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  • #3
Roadtrip, post: 5499325, member: 596960"]A particle P moves on the x-axis. At time t seconds the velocity of P is V m/s in the direction of x increasing?o
V is given by V={8t-3/2t²} for 0≤t≤4
Also V={16-2t} for t>4

Why does the acceleration have to equal zero to get the greatest speed of P in interval 0≤t≤4
Plot v-t curve for t<4.It would be a parabola open downward.Velocity is maximum at maxima of the curve.Maybe now you can understand why acceleration would be zero.
 
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