Question

If the relation between acceleration and time for an object is given by a=2t+4t^(2) Calculate the position of object from the origin at t=4 s.(At t=0 v=0 x=0 ) Hint: First integrate the given expression to get velocity and again integrate it to get the position.​

Answer 1

Answer:

Given equation,

a = 2t + 4t²

Multiplying both the sides by dt.

a.dt = (2t + 4t²).dt

⇒ Now, Integrate both the sides of the Equation,

v = t² + 4/3t³

Now, again multiplying both the sides by dt.

v.dt = (t² + 4/3t³).dt

Again Integrating both the sides of the equation,

S = t³/3 + t⁴/3

At t = 4 seconds,

S = 64/3 + 256/3

⇒ S = 21.33 + 85.33

∴ S = 106.67 m.

Hence, Displacement of the body is 106.67 m at t = 4 seconds.

Answer 2

Answer:

Explanation:Given equation,

a = 2t + 4t²

Multiplying both the sides by dt.

a.dt = (2t + 4t²).dt

⇒ Now, Integrate both the sides of the Equation,

v = t² + 4/3t³

Now, again multiplying both the sides by dt.

v.dt = (t² + 4/3t³).dt

Again Integrating both the sides of the equation,

S = t³/3 + t⁴/3

At t = 4 seconds,

S = 64/3 + 256/3

⇒ S = 21.33 + 85.33

∴ S = 106.67 m.

Hence, Displacement of the body is 106.67 m at t = 4 seconds.

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