A2 kg particle moves along an x axis, being propelled by a variable force directed along that axis. its position is given by x = 3 m+(4 m/s)t+ct2 – (2 m/s3)t3, with x in meters and t in seconds. factor c is a constant. at t = 3 s, the force on the particle has a magnitude of 36 n and is in the negative direction of the axis. what is c?

Explanation:

It is given that,

Mass of the particle, m = 2 kg

Force acting on the particle, F = -36 N (negative axis)

The position of the particle as a function of time t is given by :

Velocity,

Acceleration,

At t = 3 s

Force acting on the particle is given by :

F = ma

On solving above equation, . It has a unit same as acceleration.

Hence, this is the required solution.

Explanation:

The acceleration experimented by the 2 kg particle at t = 3 s. is:

The acceleration function is found by differentiating the position function twice:

The value of c is:

the force required to move the cart is divided by three or 33.33 n.

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