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what does the intercept of the position vs. time graph represent?What does the intial slope represent

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What is the difference between average acceleration and instantaneous acceleration.

instantaneous acceleration is the acceleration at a certain time, average acceleration is the overall average during a time period.

Why are units of acceleration meters per second squared?

acceleration is the rate of change of velocity, so it has units of velocity per time. The SI units are thus m/s per second, which in shorthand is written m/s/s or m/s2.

The brakes on a train create constant deceleration regardless of how fast its going, if the speed of the train is doubled how does this affect the time it takes the train to stop?

The time required for a train to stop is If the initial speed of the train is doubled, the time required for it to stop will double as well.

If the velocity of a ball is zero at any given instant of time can its acceleration at that instant be positive? Explain.

Yes, it is possible for an object to have a positive acceleration and a zero velocity. An object's acceleration and its velocity are distinct. For instance, if a ball is thrown straight upward, it momentarily comes to rest while still accelerating at 9.81 m/s2 downward.

If the velocity of the ball is positive can its acceleration be negative. Give example and explain.

Yes, it is possible for an object to have a positive velocity and a negative acceleration. An object's acceleration and its velocity are distinct. For instance, if a ball is thrown straight upward, during the upward journey it has an upward velocity (we'll call upward the positive direction) and a downward acceleration of −9.81 m/s2.

An object moves with a constant speed. what is the shape of it's velocity vs. time graph.

An object that moves with a constant acceleration has a linear velocity-time graph because it changes its velocity by the same amount for equal time intervals.

An object has a position time graph that is a straight line with a negative slope is the acceleration of this positive negative or zero?

An object with a position-time graph that is a straight line with a negative slope is traveling with a constant, negative velocity. (Any acceleration would produce a curvature to the position-time graph. Because the graph is a straight line the acceleration must be zero.)

Is it possible to round a corner with a constant speed/acceleration? Explain.

Speed is independent of direction, so yes, it is possible to round a corner with constant speed. However, any change in direction of motion will also change the velocity, so no, it is not possible to round a corner with constant velocity.

An object moves with a constant, negative acceleration. what is the shape of the position vs time graph? Explain.

The acceleration of an object produces curvature in its position-time graph. Any object with negative acceleration has a downward curvature to its position-time graph. Because the acceleration is constant we know the curve is a parabola.