on a v-t graph constant speed appears as a ---------line? vertical, horizontal, sloped, curved?

Answer 1

When v is the ordinate and t is the abscissa, a constant velocity would stay at v = V, some fixed value (a constant) no matter what t equals.

Say you're doing v = 90 mph in a 35 mph speed zone. At t = 0, the time the patrolman starts to clock you, you are doing v0 = 90 mph. One minute later (at t = 60 sec), you are still doing v0 = v1 = 90 mph. Thus, on the ordinate, you mark a point (0,90) for t = 0 and v = 90. Then, 60 seconds later, you mark a point (60,90) and draw a line between the two points.

That drawn line is parallel (horizontal) to the abscissa because the y distance on the graph is v0 = v1 = 90 mph at both t = 0 and t = 60 sec.

By definition, the slope of your v-t graph is a = (v1 - v0)/t, which is just the difference in velocities (v0 and v1) realized in time t. We call this slope "acceleration" when the ordinate is velocity and the abscissa is time. In this case, a = (v1 - v0)/t = (90 - 90)/60 = 0 mph/sec and the slope is flat; that is, parallel with the X axis or abscissa.

But what if you saw that patrolman at t = 0 and thought you could outrun him, you are, after all, driving a Lamborghini. So you put the pedal to the floor and now you are at v1 = 120 mph at t = 60 sec. Thus, the y-distance at t = 60 is 1/3 higher than at t = 0. In that 60 seconds elapsed time, your Lamborghini accelerated a = (v1 - v0)/t sec = (120 - 90)/60 sec = 30/60 mph/sec = 1/2 mph/sec. The slope is upward to the right because the velocity at v1 > v0; so that a > 0.

So, there you have it. when there is acceleration, the line between two (t,v) points will have slope greater than zero. When there is no acceleration, slope will be zero (a = 0) and that line will be parallel to the abscissa.

(Oh, by the by, your Lamborghini needs a tune up...you should be able to do at least 15 mph/sec in a Lam.)

Answer 2

horizontal