What is the speed and acceleration of a motorcycle traveling up a curve at t=5s?

In summary, the problem is asking for the speed and acceleration of a motorcycle that is initially traveling at 1m/s at point A (x=0) and then has its speed increased by 0.1m/s^2 at the instant t=5s. The curve that the motorcycle is traveling on is described by the equation y=0.5x^2. The solution involves taking the derivative of the position equation to find velocity and acceleration, and also considering the effects of normal acceleration, tangential acceleration, and gravity (9.81m/s^2).
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Homework Statement



A motorcycle is traveling at 1m/s when it is at A (x=0). If the speed is then increased at a=0.1m/s^2, determine the speed and acceleration at the instant t=5s.

The curve that its traveling up is y=0.5x^2

The Attempt at a Solution



I assume that we need to take the dirivative of the position to get velocity and acceleration. The only thing is that I realize the curve is given in terms of x (displacement) instead of time. I think I need to somehow relate the equation of the curve in terms of time?

On my FBD, I know we have an normal accel, tangential accel, and an accel due to gravity (9.81m/s^2).

So far that's as far as I have gotten logically.
 
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  • #2
I know this is a basic mechanics question but I'm just not sure how to start. Any help would be much appreciated.
 

FAQ: What is the speed and acceleration of a motorcycle traveling up a curve at t=5s?

What is meant by "accelerating up a curve"?

"Accelerating up a curve" refers to the process by which an object increases its velocity while moving along a curved path. This can be achieved through a combination of increasing speed and changing direction.

How does acceleration affect an object moving along a curve?

Acceleration affects an object moving along a curve by changing its velocity, which is the speed and direction of its motion. When an object accelerates up a curve, its velocity increases in the direction of the curve.

What factors contribute to an object's ability to accelerate up a curve?

The ability of an object to accelerate up a curve depends on several factors, including its mass, the curvature of the curve, and the amount of force applied to the object. Objects with lower mass and greater force applied to them will have an easier time accelerating up a curve.

Are there any real-life examples of accelerating up a curve?

Yes, there are many real-life examples of accelerating up a curve. One common example is a car or bike navigating a curved road. The vehicle must accelerate in order to maintain its speed while changing direction along the curve. Another example is a rollercoaster, which accelerates up a curve at the bottom of a loop to maintain its motion and continue along the track.

Can an object accelerate up a curve without changing its speed?

No, an object cannot accelerate up a curve without changing its speed. Acceleration, by definition, involves a change in velocity, which includes both speed and direction. In order for an object to accelerate up a curve, it must change its speed while also changing its direction of motion.

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