Your velocity is given by v( t) = t2 + 6 in m/sec, with t in seconds. Estimate t

Question

Your velocity is given by v( t) = t2 + 6 in m/sec, with t in seconds. Estimate the distance, S, traveled between t = 0 and f = 5 . Use an overestimate with data every one second. The distance is approximately m. Two cars travel in the same direction along a straight road. The figure below shows the velocity, V, of each car at time t. Car B starts 2 hours after car A and car B reaches a maximum velocity of 55 km/hr. For approximately how long does each car travel? Car A: hours Car B: hours Estimate car A's maximum velocity. km/hr Approximately how far does each car travel? Car A: km Car B: km

Explanation / Answer

3. s = integral (v(t)dt) from 0 to 5

= t^3/3 + 6t from 0 to 5 = 5^3/3 + 6*5 = 71.667 m

4. a car A- 8 hrs ; car B-4 hrs

b.max velocity of A=2*Vb =110km/hr

c.s= area under graph= area of triangle = 0.5*base * altitude

So, for car A, s = 0.5*110*8=440km

for car B, s = 0.5*55*4 = 110km

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