The velocity of a particle is given by the function v(t)=t^2-7t+1027 , where the velocity is measured in meters per second. Determine the total displacement of the particle and the total distance travelled by the particle in the first ten seconds of its travel. Give exact answers, and provide units on your final answer.

Find the following for path A in the figure below. (For each answer, enter a number.) A 0 (a) the distance traveled (in m) m t с D (c) the displacement (in m) from start to finish m B 24 68 8 10 12 displacement x (m) (b) the magnitude of the displacement (in m) from start to finish m i

In meters, what is the displacement traveled fromt = 10 sec to t = 25 sec? To correctly calculate the answer, you must determine the total area of this section. Enter your answer as an integer, not a fraction. 20 15 + 10 10 15 20 25 t(sec) -5 -10 -15 -20 v(m/sec) in

A person running through the forest with equation: y(x, t) = (1.1 m)cos(3.1x – 7.1t) for which x has units of meters and t has units of seconds. Calculate the speed of the person running in  m/s. Include postive or negative sign in the answer to show which direction the person is moving in

An object is dropped from rest and takes 2.42 seconds to reach the ground below. From what distance above the ground was it dropped? State this as a positive number and assume it has proper SI Units.

The velocity of an object is given by, = u + at V ds dt. where, u is the initial velocity, a is the acceleration, and ₺ is the time in seconds. Solve the differential equation to obtain the displacement, s, given that at t = 0, s = 7 (metres) : 1 if u = 3 ms ¹, a = 2.4 ms 2, calculate the displacements at t = 4.9 seconds. Give your answer to 2 decimal places.

A piece of wood moves at a velocity (measured in millimeters per year) of v(1) = r² – 3t – 4 where 1 = 1 would be the end of the first year. If a is the displacement of the wood in the first 5 years and b is the distance traveled in the first 5 years, what is a- b? None of the listed answers

The following times are given using metric prefixes on the base SI unit of time: the second. Rewrite them in scientific notation without the prefix (in s). For example, 47 Ts would be rewritten as 4.7 ✕ 1013 s. (Enter your answers as m ✕ 10n, where 1 ≤ |m| < 10  and n is an integer.) 984 Ps 986 fs 19 ns 572 µs

After conducting the signal speed experiment a student has recorded the following data. L₂ (m) 1.5 3 4.5 8 15 30 dt (ns) 6.50 13.72 21.02 38.10 72.20 145.42 L2 is the length of the longer cable in meters and dt is the measured time delay in nanoseconds. The student neglected to record L₁, the length of the shorter cable. After speaking with their instructor, they learn all is not lost. They know the speed of the signal can be calculated based on the distance traveled divided by the time. However, the recorded times measure how much longer the signal had to travel in L2 compared to L₁. A little bit of thought convinces them (correctly) that

Bicyclists in the Tour de France reach speeds of 500 miles per hour (mi/h) on flat sections of the road. What is this speed in kilometers per second (km/sec)? cf. 1 mile = 1.609 km