A particle travels along a straight line with a velocity v = (12 - 3t) m/s, where t is in seconds. When t = 1 s, the particle is located 10 m to the left of the origin. Determine the acceleration when t = 4 s. the displacement from t = 0,t = 10 s, and the distance the particle travels during this time period. a 9 2. A sphere is fired downwards into a medium with an initial speed of 27 m/s. If it experiences a deceleration of a = (-6t) m/s2 ,where t is in seconds, determine the distance traveled before it stops.

(1).The acceleration is -24 m/s²

The total distance is 912 m.

(2). The distance traveled before it stop is 78 m.

Explanation:

Given that,

Velocity = (12-3t^2) m/s

When t = 1 s, the particle is located 10 m to the left of the origin.

We need to calculate the acceleration at t = 4 sec

Using formula of acceleration

Put the value of v

Put the value of t

The displacement from t = 0,t = 10 s, and the distance the particle travels during this time period.

We need to calculate the distance

Using formula of distance

Put the value of v

At t = 0,

At t = 10,

The displacement is

The distance at t= 2 sec

The total distance will be,

(2). We need to calculate the distance at 2 sec

Using equation of motion

Put the value into the formula

Hence, (1).The acceleration is -24 m/s²

The total distance is 912 m.

(2). The distance traveled before it stop is 78 m.

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