Suppose a car is moving with variable acceleration. Equation of its velocity-time graph is y=x^4
>Find its distance travelled between 1st and 3rd second.
>Find its distance travelled between 4th and 5th second.
>Find its distance travelled between 1st and 3rd second.
>Find its distance travelled between 4th and 5th second.
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The distance it traveled can be expressed with it's integral.
y = x⁴
d = ∫₁³ x⁴ dx
d = 1/5x⁵ |₁³
d = 1/5(3)⁵ - 1/5(1)⁵
d = 242/5
Part two can be done with the same integral, over a different bound.
y = x⁴
d = ∫₁³ x⁴ dx
d = 1/5x⁵ |₁³
d = 1/5(3)⁵ - 1/5(1)⁵
d = 242/5
Part two can be done with the same integral, over a different bound.
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total distance traveled = ∫ x^4 dx [1,3] = 242/5
b) d = ∫ x^4 dx [1,5] - 242/5 = 3124/5 - 242/5 = 2882/5 = 576.40
b) d = ∫ x^4 dx [1,5] - 242/5 = 3124/5 - 242/5 = 2882/5 = 576.40