Physics and Natural Sciences questions and Essay (Essay Sample)

Physics and Natural Sciences questions and Essay Name Institution Course Instructor Date Question 1) a) Time dependence of velocity and acceleration of the particle: Given: V = α Velocity (V): V is equal to α. Since α is a constant, the velocity does not change with time. It remains constant at V = α. Acceleration (a): Acceleration (a) is the derivative of velocity with respect to time: a = dvdt Given V = α, dadt = 0 Therefore, acceleration (a) is zero, a = 0. b) Average velocity during the first S meters: Average velocity (V̄): V̄ = Total displacementTotal time taken Given the particle starts from x = 0 and moves S meters with a constant velocity α, the time t it takes to travel S meters is: t = Sα The average velocity (V̄) over this interval is the same as the constant velocity α since the velocity does not change over time. Therefore: V̄ = α The average velocity (V̄) of the particle during the time it runs the first S meters along its path is α, the same as its constant velocity. Question 2) The electric field (E) at the center due to a uniformly charged half-ring is given by: E = kqnR2 where: k is Coulomb's constant (8.9875 × 109Nm2/C2), q is the total charge, R is the radius of the half-ring. Given: q = 0.7 nC = 0.7 × 10−9 C, R = 20 cm = 0.2 m. Substituting the given values into the formula: E = 8.9875 × 109×0.7 × 10−9π×0.22 E =8.9875×0.7π×0.04 E =6.291250.1256 E ≈ 50.1 N/C Therefore, the magnitude of the electric field strength at the center of curvature of this half-ring is approximately 50.1 N/C. Question 3) Mars Exploration Rovers (MER) Mission The Mars Exploration Rovers (MER) venture by NASA in 2003 was aimed at scrutinizing the history of water on the red planet, studying geology to find evidence of the past environment, and discovering early signs of life. Two rovers, namely Spirit and Opportunity, that were landing on two different places separated on Mars were sent to do that job (Crisp et al., 2013). The original motivation for sending MER mission was to establish the presence of water either in the past or at the moment and to evaluate the potential Mars habitats. The rovers come with a set of equipment including wide-angle cameras, spectrometers, and RATs, the rock abrasion tool for short. These devices provided samples from the Martian Rocks, Soil, and Atmosphere to a deeper extent had been a big help in abstracting the planet's past and the chance of its life existence(D'Amario, 2006). Among the most remarkable discoveries made by MER are the traces of the former aqueous activity on Mars. Both Spirit and Opportunity uncovered geological formations such as rocks consisting of layers and hematite-rich so-called "blueberries" that all point to Mars' an...