A particle with mass m = 1.5 is moving along a straight trajectory. The distance

Question

A particle with mass m = 1.5 is moving along a straight trajectory. The distance covered by a particle is described by the function S(t) = t^3 +1, where t > 0 is the time. Kinetic energy E of a particle is given by E = mv^2/2, where v is the particle speed. Find a function that describes the kinetic energy of this particle. Find kinetic energy of the particle at time t = 10. What is the distance covered by the particle by time t = 7? Find approximate value of time t when the speed of the particle is 25. Find a function that describes the acceleration of this particle. Find the acceleration of the particle at t = 6. Find the time when the acceleration of the particle is 18.

Explanation / Answer

here,

mass of the particle , m = 1.5 kg

S(t) = t^3 + t

differentiating the equation we get

v(t) = 3*t^2 + 1

(a)

the kinetic energy , KE = 0.5 * m * v^2

KE = 0.5 * 1.5 * ( 3 * t^2 + 1)

KE = (2.25 * t^2 + 0.75 ) J

the kinetic energy of the particle is (2.25 * t^2 + 0.75 ) J

(b)

at t = 10 s

E = (2.25 * t^2 + 0.75 ) J

E = 2.25 * 10^2 + 0.75

E = 225.75 J

the kinetic energy of the particle is 225.75 J

(c)

s = t^3 + t

at t = 7

s = 7^3 + 7

s = 350 m

the distance covered by the particle is 350 m

(d)

v(t) = 3*t^2 + 1

when v = 25 m/s

25 = 3 * t^2 + 1

t = 2.83 s

the value of time is 22.83 s when speed is 25 m/s

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