Problems about calculating acceleration,velocity

[acelya]

Homework Statement

A car, as shown in the figure, is going in a curvilinear road. The size of the car will be neglected.

Homework Equations

Its acceleration is a = 0.5*e^t m/s^2.

The Attempt at a Solution

If it goes 18 meters on its way, then calculate its velocity and acceleration.

I have one more question. A particle is making linear action. Its velocity in the origin is 4 m/s. If particle is slowing down with acceleration a = -3/2*v^1/2 m/s^2, calculate the elapse time and its taking way until it stops(v=0).

Hope I could explain my questions clearly. How can I calculate them? Please help me.

 

[Doc Al]

Its acceleration is a = 0.5*e^t m/s^2.

I assume that is the tangential acceleration.

If it goes 18 meters on its way, then calculate its velocity and acceleration.

Given acceleration, how do you find velocity and distance?

 

[acelya]

Yes, that is the tangential acceleration.

I don't know how can I find their values, bacause it is going on a curvilinear road and there is a p value (you can see in the figure) p=30m. I must use this value of p.

 

[Doc Al]

Yes, that is the tangential acceleration.

I don't know how can I find their values, bacause it is going on a curvilinear road and there is a p value (you can see in the figure) p=30m. I must use this value of p.

You'll use the radius to find the centripetal component of the acceleration.

But first things first. How can you find the velocity and distance, given the tangential acceleration? Hint: Calculus.

 

[acelya]

I must use the integral. Distance velocity v=0.5e^t+c1 and distance x=0.5e^t+c1t+c2 (c1,c2 constant values). But then, it is going 18 meters on the road.

 

[Doc Al]

I must use the integral. Distance velocity v=0.5e^t+c1 and distance x=0.5e^t+c1t+c2 (c1,c2 constant values). But then, it is going 18 meters on the road.

Good. What are c1 and c2? (Those depend on the initial conditions.)

 

[acelya]

But I don't know where the car was on the road firstly. If at t=0, it was in origin, then c1=-0,5 , c2=0. But, this question don't tell us it was in the origin at first.

 

[Doc Al]

But I don't know where the car was on the road firstly. If at t=0, it was in origin, then c1=-0,5 , c2=0. But, this question don't tell us it was in the origin at first.

You have to know the initial velocity and position or be able to make reasonable assumptions. That it starts from rest and at x = 0 seems reasonable. How did you get c2 = 0?