Question #126301

A train starting at station A moves along a straight line and stops at station B; distance x of the train from the starting point varies with time t as x= 3/4t^2- t^3/4

Find distance between station A and station B

i) 1unit ii)2 units iii) 1/2 unit

Find maximum velocity of the train.

i)3/4 unit ii)3/2 unit iii)1/4 unit

please show all the steps along with explanation and reply asap

Find distance between station A and station B

i) 1unit ii)2 units iii) 1/2 unit

Find maximum velocity of the train.

i)3/4 unit ii)3/2 unit iii)1/4 unit

please show all the steps along with explanation and reply asap

Expert's answer

Find distance between station A and station B for the given units of time:

i) If it takes 1 unit of time to travel from A to B, the distance is

ii) If it takes 2 units of time to travel from A to B, the distance is

ii) If it takes 1/2 units of time to travel from A to B, the distance is

To find the maximum velocity of the train, determine the equation for the velocity from the equation of displacements:

To find at what moment the velocity was maximum, equate the derivative of velocity to zero and find time:

However, we are given smaller values. For these cases, the velocity was

i) 3/4 unit

ii) 3/2 unit

iii) 1/4 unit

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