The Starship Enterprise returns from warp drive to ordinary space with a forward speed of 51 km/s. To the crew's great surprise, a Klingon ship is 150 km directly ahead, traveling in the same direction at a mere 21 km/s. Without evasive action, the Enterprise will overtake and collide with the Klingons in just about 5.0 s. The Enterprise's computers react instantly to brake the ship. PART A. What magnitude acceleration does the Enterprise need to just barely avoid a collision with the Klingon ship? Assume the acceleration is constant.
A particle's velocity is described by the function vx=kt2, where vx is in m/s, t is in s, and k is a constant. The particle's position at t0=0s is x0 = -7.90 m . At t1 = 1.00 s , the particle is at x1 = 8.70 m .
A toy train is pushed forward and released at x0=2.0m with a speed of 2.0 m/s. It rolls at a steady speed for 2.0 s, then one wheel begins to stick. The train comes to a stop 6.0 m from the point at which it was released.
To understand the meaning of the variables that appear in the equations for one-dimensional kinematics with constant acceleration. Motion with a constant, nonzero acceleration is not uncommon in the world around us. Falling (or thrown) objects and cars starting and stopping approximate this type of motion. It is also the type of motion most frequently involved in introductory kinematics problems. The kinematic equations for such motion can be written as x(t)=xi+vit+12at2, v(t)=vi+at, where the symbols are defined as follows: x(t) is the position of the particle; xi is the initial position of the particle; v(t) is the velocity of the particle; vi is the initial velocity of the particle; a is the acceleration of the particle.
A common graphical representation of motion along a straight line is the v vs. t graph, that is, the graph of (instantaneous) velocity as a function of time. In this graph, time t is plotted on the horizontal axis and velocity v on the vertical axis. Note that by definition, velocity and acceleration are vector quantities. In a straight-line motion, however, these vectors have only a single nonzero component in the direction of motion. Thus, in this problem, we will call v the velocity and a the acceleration, even though they are really the components of the velocity and acceleration vectors in the direction of motion, respectively. Here is a plot of velocity versus time for a particle that travels along a straight line with varying velocity. Refer to this plot to answer the following questions.
As you look out of your dorm window, a flower pot suddenly falls past. The pot is visible for a time t, and the vertical length of your window is Lw. Take down to be the positive direction, so that downward velocities are positive and the acceleration due to gravity is the positive quantity g. Assume that the flower pot was dropped by someone on the floor above you (rather than thrown downward).
To demonstrate the tremendous acceleration of a top fuel drag racer, you attempt to run your car into the back of a dragster that is "burning out" at the red light before the start of a race. (Burning out means spinning the tires at high speed to heat the tread and make the rubber sticky.) You drive at a constant speed of v0 toward the stopped dragster, not slowing down in the face of the imminent collision. The dragster driver sees you coming but waits until the last instant to put down the hammer, accelerating from the starting line at constant acceleration, a. Let the time at which the dragster starts to accelerate be t=0.
Tim and Rick both can run at speed vr and walk at speed vw, with vr>vw. They set off together on a journey of distance D. Rick walks half of the distance and runs the other half. Tim walks half of the time and runs the other half.
Julie drives 100 mi to Grandmother's house. On the way to Grandmother's, Julie drives half the distance at 35.0 mph and half the distance at 65.0 mph. On her return trip, she drives half the time at 35.0 mph and half the time at 65.0 mph. PART A. What is Julie's average speed on the way to Grandmother's house?
A particle moving along the x-axis has its position described by the function x =( 2.00 t3− 5.00 t+ 3.00 )m, where t is in s. At t= 3.00, what are the particle's (a) position, (b) velocity, and (c) acceleration?