Why Does the Acceleration of a Particle Need to Be Zero for Maximum Speed?

[Roadtrip]

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

 

[Dale]

This is probably best understood by plotting the velocity. Look at the maximum, and see what the slope is visually.

 

[harsh_sinha]

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.