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The accelaration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an intial velocity vo. The distance travelled at time t is

The accelaration of a particle is increasing linearly with time t as bt. The particle starts from the origin with an intial velocity vo. The distance travelled at time t is

Grade:11

2 Answers

Arun
25750 Points
3 years ago
Given the acceleration as a function of time:
 
a(t)=bt
 
Integrate to obtain the velocity as a function of time.v(t)={\frac{1}{2}}bt^2+C 
 
 We are told that the constant of integration is V0
 
v(t)={\frac{1}{2}}bt^2+V_{0}
 
Integrate, again, to obtain the displacement as a function of time.d(t)=16bt^3+V_{0}t+c
 
The phrase "starts from the origin" tells us that the integration constant is 0:
 
d(t)=16bt^3+V_{0}t
 
 
Saurabh Koranglekar
askIITians Faculty 10335 Points
3 years ago
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