Finding velocity of a Formula one race car!

Classical Mechanics Level 2

credit:Wikipedia(with license for reuse and modification) credit:Wikipedia(with license for reuse and modification)

The displacement traversed by a Formula One race car is modeled by the function s ( t ) = t 3 − 2 t 2 + 5 t − 3. s(t)=t^3-2t^2+5t-3. Find the velocity of the car at t = 5 t=5 .


The answer is 60.

Sravanth C. by Sravanth C. , 21, India

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1 solution

Sravanth C.
Mar 2, 2016

We know that the velocity of an object is the derivative of the displacement function:

v ( t ) = d s d t = d d t ( t 3 − 2 t 2 + 5 t − 3 ) = 3 t 2 − 4 t + 5 v(t)=\dfrac{ds}{dt}=\dfrac{d}{dt}(t^3-2t^2+5t-3)=3t^2-4t+5

Thus substituting t = 5 t=5 we get:

v ( 5 ) = 3 × 5 2 − 4 × 5 + 5 = 75 − 20 + 5 = 60 m / s v(5)=3\times 5^2-4\times 5+5\\=75-20+5=\boxed{60m/s}

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I have question may be its a silly one why don't we first substitute t=5 in S(t) function and then find the velocity

Naresh Goud - 3 years, 7 months ago

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No problem learning is a process.

The velocity of a body is defined as the change in distance by the time taken. Bodies with uniform velocities have linear displacement functions like s ( t ) = k t s(t)=kt .

But when this function isn't linear, we cannot directly find the velocity, we need to differentiate the function. For more information read equations of motion and limits of functions - problem solving

Sravanth C. - 3 years, 4 months ago

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