Aparticle moves along a straight line so that its velocity, v ms^-1, at time t seconds is given by v=240+20t-10t^2, for 0≤t≤6.
(i) find the value of t when the speed of the particle is greatest.
(ii) find the acceleration of the particle when its speed is zero.

(i) The speed of the particle is greatest at t=1 and maximum speed is 500 m/s.

(ii) The acceleration of the particle is -100 when its speed is zero.

Step-by-step explanation:

(i)

We need to find the the time at which time at which the speed of the particle is greatest. It means we need to find the value of t at which velocity function is maximum.

If a function is , then the vertex of the function is

The given velocity function is

For 0≤t≤6.

Here, a=-10, b=20 and c=240.

The leading coefficient is negative it means the vertex of the velocity function is the point of maxima.

At t=1,

Therefore, the speed of the particle is greatest at t=1 and maximum speed is 500 m/s.

(ii)

Equate the velocity function equal to zero, to find the time at which speed is zero.

Splitting the middle term we get

Using zero product property,

Time can not be negative. So, at t=6  the speed is zero.

Differentiate the velocity function with respect to t.

Substitute t=6 in the above function.

Therefore the acceleration of the particle is -100 when its speed is zero.

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step-by-step explanation: