A particle moves along a straight line and its position at time t is given by s(

Question

A particle moves along a straight line and its position at time t is given by s(t) = t4 - 7t + 20, t 0. where s is measured in feet and t in seconds. Find the velocity at time t: 4*t^3-7 Find the velocity (in ft/sec) of the particle at time t = 3. 101 Find all values of t for which the particle is at rest. (If there are no such values, enter none . If there are more than one value, list them separated by commas.) t = Use interval notation to indicate when the particle is moving in the positive direction. (If needed, enter inf for infinity. If the particle is never moving in the positive direction, enter none .) Find the total distance traveled during the first 8 seconds.

Explanation / Answer

s(t)=t^4-7t+20

s'(t)=v(t)= 4t^3 - 7...........

so, v(3)= 101 ft/s...

particle is at rest ,

so v(t)=0..

4t^3-7=0

t^3=7/4.

t=1.2 seconds...............

for positive s......... we have to get.... t^4-7t+20>0

which is possible for all t......

total distance= intrgral(s(t)) from 0 to 8 seconds....

by which we get..

total distance travelled to be = 6489.6 feet..........

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