The accompanying figure shows the velocity v = ds/dt = f(1) (m/sec) of a body moving along a coordinate line. v (m/sec) v = f(t) AA. 3 t (sec) 1 4 6/ 8 10 -3
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- I need help with a math question: Given that x = position, v = velocity, a = acceleration, m = mass. Which of the following will have units of kg * m/s^2 and why? m ∫ a dt m ∫ v dt 1/2m dv^2/dx m ∫ x dt 1/2m dv^2/dt m dx/dt m dv/dt m da/dt 1/2m ∫ v^2 dt I am including an image/reference table. Thanks!3) The upward velocity of the rocket is measured with respect to time and the data is given in the following table. Velocity vs time data for a rocket Time, t(s) Velocity, V (m/s) 105.7 8. 175.2 12 278.2 We wanted to approximate the velocity profile by v(t=at*+bt+c,5sts12 Please construct the set of linear equation and solve the equation for the coefficients a, b and c in v (t).The velocity of a rocket is given as a function of time by v(t) = A(1 – e-bt) for 0 , t , 30 s, where the constants A = 150 and b = -0.15. [ d/dx (e-ax dx) = -a e-ax; ∫ e-ax dx = -1/a e-ax ] a) What are the SI units of A and b? b) What is the speed of the rocket at t = 10 s? c)Find the displacement of the rocket in the first 10 s ( from t = 0 s to t = 10 s)
- A high-speed aircraft takes-off in the xyz-plane and the coordinates are given by x(t) = αt, y(t) = 3.0 m − βt^2, and z(t) = αt − γt^3, where α = 2.4 m/s, β = 1.2 m/s^2, and γ = 0.6 m/s^3. Calculate:a) The velocity and acceleration vectors of the high-speed aircraft as functions of time.b) The magnitude of the high-speed aircraft’s velocity and acceleration after 2 sec.A car is initially at rest on a straight road. The graph shows the speed of the car as a function of time. v (m/s) 12 11 10 9 8 7 6 5 4 3 2 1 M Ħ 0 1 2 3 4 5 6 7 8 9 10 11 t(s) What is the speed of the car at t=7 s? Submit Answer Tries 0/12 How much distance did the car cover in the first 9 seconds? 12 13 14 Submit Answer Tries 0/12 Determine the distance covered by the car between t=10 s and t=13 s? Submit Answer Tries 0/12 What is the average speed of the car between t=4 s and t=8 s? Submit Answer Tries 0/12Let V1 = -6.4 i^ + 8.1 j^ and V2 = -4.5 j^ + 4.4 i^. Determine the magnitude of abs.(V1+V2)
- The acceleration of a particle is a constant. At t=0 the velocity of the particle is (14.91 + 18.4ĵ) m/s. At t = 4.6 s the velocity is 11.4j m/s. (Use the following as necessary: t. Do not include units in your answers.) (a) What is the particle's acceleration (in m/s²)? = î+ 18.4 v(t) = (b) How do the position (in m) and velocity (in m/s) vary with time? Assume the particle is initially at the origin. r(t) = î+ X Î- i) m/s m/sThe velocity-time graph that describes the velocity of an object with time is given as in the figure below. if the values of a= 82.3, b=126.9 and c=53.4, Find the average acceleration ( in units of km/h²) of the object over the tie period [0, 2] h. v(km/h) b a t(h) 0.5 1.0 1.5 2.0 Select one: O A. 98.0 Ов. 106.8 Ос. 67.8 OD. -14.4 O E. -115.6Given the figure below and if the mass of the beam is 170 g and L1 = 300 mm, determine: (a) M2 if M1 = 990 g, M3 = 170 g, L2 = 400 mm and L3 = 220 mm, and (b) L3 if M1 = 890 g, M2 = 420 g, M3 = 220 g and L2 = 200 mm M₁ L₁ ↓ L2 1000mm M₂ La M₂
- Question 1: Complete the calculations of the table based on the data given below Test No Weight (N) H, (cm) H2 (cm) P.E. (initial) (J) P.E. (final) (J) Loss in P.E. (J) 1 1.8 60 43.0 1.08 0.774 0.306 2 2.0 60 44.4 1.2 0.888 0.312 3 2.2 60 45.7 1.32 1.005 0.315A graph of x vs. t4, with x on the vertical axis and t4 on the horizontal axis, is linear. Its slope is 31 m/s4 and its vertical-axis intercept is 8 m. Write an equation for x as a function of t. x = (31 m/s 4 )t 4 + 8 m x = (8 m )t 4 − 31 m/s 4 x=(31 m/s48 m)t4x=31 m/s48 mt4 x = (8 m )t 4 + 31 m/s 46.00k, with t in seconds and r in meters. An electron's position is given by 7 = 4.00tî – 5.00t2 ĵ + (a) In unit-vector notation, what is the electron's velocity v (t)? (Use the following as necessary: t.) V (t) = m/s (b) What is v in unit-vector notation at t = 5.00 s? v(t = 5.00) = m/s (c) What is the magnitude of v at t = 5.00 s? m/s (d) What angle does v make with the positive direction of the x axis at t = 5.00 s? ° (from the +x axis)