A vehicle travels in a fixed direction at a velocity v(t) that varies with time as...

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A vehicle travels in a fixed direction at a velocity v(t) that varies with time as follows: t₁ < t <t₂ t>t₂ v(t) = At² v(t)=CB(t-t₂)² v(t) = v₂. Here A, B, C and v2 are constants. (a) Find A. B and C such that both the velocity and acceleration are continuous at t = t₁ and t = t₂. (b) Sketch the velocity and acceleration as a function of time. (c) Find the total distance travelled between t = 0 and t = t3, where tą > 12. [3] [3] [4] A vehicle travels in a fixed direction at a velocity v(t) that varies with time as follows: t₁ < t <t₂ t>t₂ v(t) = At² v(t)=CB(t-t₂)² v(t) = v₂. Here A, B, C and v2 are constants. (a) Find A. B and C such that both the velocity and acceleration are continuous at t = t₁ and t = t₂. (b) Sketch the velocity and acceleration as a function of time. (c) Find the total distance travelled between t = 0 and t = t3, where tą > 12. [3] [3] [4]

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